Course:

Software Engineering II

academic year: 2007-2008Course Web-site: [www.di.univaq.it/

cortelle/]

Lecturer: Catia Trubiani

Computer Science Department University of L'Aquila - Italy

Catia.trubiani@di.univaq.it

Lecture 21: Performance Modeling with GSPNs

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Copyright Notice

» The material in these slides may be freely reproduced and distributed, partially or totally, as far as an explicit reference or acknowledge to the material author is preserved.

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Roadmap

Performance

modeling

evaluationGeneralized

Stochastic Petri Nets (GSPNs)

Symbolic Hierarchical Automated Reliability and

Performance Evaluator (SHARPE)

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Software Performance

Software developers’ world (vocabulary) is intrinsically distant from performance analysts’ one.

APPLICATIONMODEL

APPLICATIONPERFORMANCE

MODEL

APPLICATIONPERFORMANCE

MODEL

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Performance Notations

Markov process

es

Queueing

Networks

Generalized

Stochastic Petri Nets Stochast

ic Process Algebras

Simulation

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Performance Model Elements : GSPNs

ARC WEIGHTS

Graphical Notation

PLACES

MARKING

X

Px

FLOW

RELATION

TRANSITIONS

Symbols Description

The number of tokens in places defines the marking of the net at a certain time

Arc weights are numbers associated to arcs

The arcs are input, output, or inhibitor and represent the link between places and transitions

Transitions are immediate or timed and represent the system changing state

Places are locations that represent (possibly partial) states of a system

timm ttimed

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GSPNs formal definition

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S = ( P , T , I , O , H , M0 )

P1

PLACES INITIAL

MARKING

INPUTTRANSITIONS

(immediate

P2

P3

2

P4

4

t1 t2

or timed)

OUTPUT

INHIBITION

2

PN system

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GSPNs incrementally

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P1

P2

P3

t12

2

1

P1

P2

P3

t1

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1

P1

P2

P3

t1

2

t2

3

Petri Net

Stochastic Petri Net

Generalized Stochastic Petri Net

P4

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GSPNs more formal

P is set of placesT is set of transitions, T ∩ P = Ø

I, O, H : T -> Bag(P) with Bag(P) multiset on P

Mo : P ->

t = { p E I (t,p) > 0 } input arcs t = { p E O (t,p) > 0 } output arcs °t = { p E H (t,p) > 0 } inhibitor arcs

S = ( P , T , I , O , H , M0 ) PN system

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GSPNs formal example

I : t1 -> P1, t1 -> P2, t2 -> P3

O : t1 -> P3, t2 -> P4

H : t2 -> P4

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P1

P2

P32 P4

4

t1 t2 2

t1 = { P1, P2 } t1 = { P3 } °t1 = Ø t2 = { P3 } t2 = { P4 } °t2 = { P4 }

P = { P1, P2, P3, P4 }T = { t1, t2 }

Mo: P1 ->3, P2 ->2, P3 ->1, P4 ->0

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GSPNs formal example

I : t1 -> P1, t1 -> P2, t2 -> P3

I(t1 -> P1) = 2, I(t1 -> P2 ) = 1, t2 -> P3 = 4

O : t1 -> P3, t2 -> P4

O(t1 -> P3) = 3, O(t2 -> P4 ) = 2

H : t2 -> P4

H(t2 -> P4) = 2

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P1

P2

P32 P4

4

t1 t2 2

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GSPNs dynamics

Rules:

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P1

P2

P3

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1

P3P1

P2

t1

t1

(1) Enabling rule - conditions under which transitions are allowed to fire.

p E t, M(p) ≥ O (t, p) p E °t, M(p) < H (t, p)

(2) Firing rule – marking modifications induced by the transition firing.

M’ = M + O(t) – I(t)

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Example – Banking System

Use Case Diagram

Central Server

ATM1

ATM2 ATMn

………

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Banking System Performance Model

Banking System (BS):

allow_request

usersarrivals

startWF

reqPD

answerWF

send_answerWF

startreqPIN

PIN_ko

PIN_ok

checkWF_ko

checkWF_ok

waitWF

rcvACK_WF

startQA

reqQA

answerQA

send_answerQA

checkQA_ko checkQA_ok

waitQA

rcvACK_QA

checkTF_ok

startTF

reqTF

answerTF

waitTF

checkTF_ko

validUser

rcvACK_TF

send_answerTF

-> WF: Withdraw Funds

-> QA: Query Account

-> TF: Transfer Funds

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PN in execution – At Restaurant(1)

» Restaurant: First scenario

- waiter takes order

from customer 1

- tell kitchen

- serves customer 1

- waiter takes order

from customer 2

- tell kitchen

- serves customer 2

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PN in execution – At Restaurant(1)

WaiterfreeCustomer 1 Customer 2

Takeorder

Takeorder

Ordertaken

Tellkitchen

wait wait

Serve food Serve food

eating eating

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PN in execution – At Restaurant(2)

» Restaurant: Second scenario

- waiter takes order

from customer 1

- tell kitchen

- waiter takes order

from customer 2

- tell kitchen

- serves customer 1

- serves customer 2

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PN in execution – At Restaurant(2)

WaiterfreeCustomer 1 Customer 2

Takeorder

Takeorder

Ordertaken

Tellkitchen

wait wait

Serve food Serve food

eating eating

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Exercise – Elevator System

» Elevator System

an hotel has two

elevators;

there are three floors

to cover;

in every floor there are

0..n users waiting for

the elevator.

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Exercise – Elevator System

1st elevator

1st floor

2nd floor

3rd floor

upTo2ndFloor

upTo3rdFloor

downTo1stFloor

downTo2ndFloor

first

second

third

Where is the elevator? What is the initial state?1st floor…

2nd floor…

3rd floor…

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Exercise – Elevator System

1st elevator

1st floor

2nd floor

3rd floor

2nd elevator

1st floor

2nd floor

3rd floor

What is the initial state?Example: 1st elevator at 2nd floor, 2nd elevator at 1st

floor

CONCURRENTSYSTEMS

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Exercise – Elevator System

1st elevator 2nd elevator

And the users?

users1stFloor

users2ndFloor

users3rdFloor

Relationship between users and elevators?

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Exercise – Computation

» Computation

a calculator has two

variables, a and b;

- the calculation is the following (a+b)/(a-b)

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Exercise – Computation

copy_a

x = (a+b)/(a-b)

copy_b

(a+b)

(a-b)

+

-

=!0

=0

/ x

ND

(a-b)

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Exercise – Coffee machine

» Coffee machine

a coffee machine

accepts 5cent or 10cent;

- the cost of products

are 15cent or 20cent;

- no change.

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Exercise – Coffee machine

insert5cent

0cent

5cent 15cent

20cent10cent

insert10centinsert5cent

insert10cent

insert10cent

insert5cent

insert5cent

take15centProduct

take20centProduct

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Exercise – Communication

» Communication

- there are two processes

able to communicate ;

- one process sends messages,

the other process receives;

- the buffer accumulates one message at once.

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Exercise – Communication

readyto send

waitfor ack

ackreceived

msgreceived

acksent

readyto receive

bufferfull

bufferfullsend

msg

receiveack

receivemsg

sendack

proc1

proc2

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Exercise – Dining Philosophers

» Five philosophers alternatively think and eating

five chopsticks

two states: philosophers eating, philosophers thinking

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Exercise – Dining Philosophers

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Basic Readings

» [Performance modeling]

M. Ajmone Marsan, Gianfranco Balbo, Gianni Conte, Susanna Donatelli, Giuliana Franceschinis “MODELLING WITH GENERALISED STOCHASTIC PETRI NETS”,